Why won't my model unwrap?
I think it is impossible to select the whole edge using Alt+RMB. It is a matter of geometry you've got there.
 What you can do is select the upper edge/vertex and then (while holding the Ctrl button) the bottom one.


You may also select the upper vertex/edge, then (holding Shift) the bottom one and then go to Select-->Shortest Path.


QUICK TIP: I figured out that your origin point is located outside the mesh. It is a good habit to keep it inside. Being in Edit Mode select the whole mesh (A), press Shift+S-->Cursor to Selected and then (being in Object Mode) Shift+Ctrl+Alt+C-->Origin to 3D Cursor to place an origin point inside a mesh.


Note: You'll probably have to delete the top and bottom ngons to make a proper unwrap. And make sure to remove the doubles (being in Edit mode select the whole mesh [A]), then press W-->Remove Doubles).

EDIT: I've unwrapped a mesh and the UV islands look like this:


Here's the .blend to download:
http://www.pasteall.org/blend/37742